1,187 research outputs found
The Liquid Blister Test
We consider a thin elastic sheet adhering to a stiff substrate by means of
the surface tension of a thin liquid layer. Debonding is initiated by imposing
a vertical displacement at the centre of the sheet and leads to the formation
of a delaminated region, or `blister'. This experiment reveals that the
perimeter of the blister takes one of three different forms depending on the
vertical displacement imposed. As this displacement is increased, we observe
first circular, then undulating and finally triangular blisters. We obtain
theoretical predictions for the observed features of each of these three
families of blisters. The theory is built upon the F\"{o}ppl-von K\'{a}rm\'{a}n
equations for thin elastic plates and accounts for the surface energy of the
liquid. We find good quantitative agreement between our theoretical predictions
and experimental results, demonstrating that all three families are governed by
different balances between elastic and capillary forces. Our results may bear
on micrometric tapered devices and other systems where elastic and adhesive
forces are in competition.Comment: 23 pages, 11 figs approx published versio
Harold Jeffreys's Theory of Probability Revisited
Published exactly seventy years ago, Jeffreys's Theory of Probability (1939)
has had a unique impact on the Bayesian community and is now considered to be
one of the main classics in Bayesian Statistics as well as the initiator of the
objective Bayes school. In particular, its advances on the derivation of
noninformative priors as well as on the scaling of Bayes factors have had a
lasting impact on the field. However, the book reflects the characteristics of
the time, especially in terms of mathematical rigor. In this paper we point out
the fundamental aspects of this reference work, especially the thorough
coverage of testing problems and the construction of both estimation and
testing noninformative priors based on functional divergences. Our major aim
here is to help modern readers in navigating in this difficult text and in
concentrating on passages that are still relevant today.Comment: This paper commented in: [arXiv:1001.2967], [arXiv:1001.2968],
[arXiv:1001.2970], [arXiv:1001.2975], [arXiv:1001.2985], [arXiv:1001.3073].
Rejoinder in [arXiv:0909.1008]. Published in at
http://dx.doi.org/10.1214/09-STS284 the Statistical Science
(http://www.imstat.org/sts/) by the Institute of Mathematical Statistics
(http://www.imstat.org
Quantum Gravity and Inflation
Using the Ashtekar-Sen variables of loop quantum gravity, a new class of
exact solutions to the equations of quantum cosmology is found for gravity
coupled to a scalar field, that corresponds to inflating universes. The scalar
field, which has an arbitrary potential, is treated as a time variable,
reducing the hamiltonian constraint to a time-dependent Schroedinger equation.
When reduced to the homogeneous and isotropic case, this is solved exactly by a
set of solutions that extend the Kodama state, taking into account the time
dependence of the vacuum energy. Each quantum state corresponds to a classical
solution of the Hamiltonian-Jacobi equation. The study of the latter shows
evidence for an attractor, suggesting a universality in the phenomena of
inflation. Finally, wavepackets can be constructed by superposing solutions
with different ratios of kinetic to potential scalar field energy, resolving,
at least in this case, the issue of normalizability of the Kodama state.Comment: 18 Pages, 2 Figures; major corrections to equations but prior results
still hold, updated reference
Sequential quasi-Monte Carlo: Introduction for Non-Experts, Dimension Reduction, Application to Partly Observed Diffusion Processes
SMC (Sequential Monte Carlo) is a class of Monte Carlo algorithms for
filtering and related sequential problems. Gerber and Chopin (2015) introduced
SQMC (Sequential quasi-Monte Carlo), a QMC version of SMC. This paper has two
objectives: (a) to introduce Sequential Monte Carlo to the QMC community, whose
members are usually less familiar with state-space models and particle
filtering; (b) to extend SQMC to the filtering of continuous-time state-space
models, where the latent process is a diffusion. A recurring point in the paper
will be the notion of dimension reduction, that is how to implement SQMC in
such a way that it provides good performance despite the high dimension of the
problem.Comment: To be published in the proceedings of MCMQMC 201
Kernel Sequential Monte Carlo
We propose kernel sequential Monte Carlo (KSMC), a framework for sampling from static target densities. KSMC is a family of
sequential Monte Carlo algorithms that are based on building emulator
models of the current particle system in a reproducing kernel Hilbert
space. We here focus on modelling nonlinear covariance structure and
gradients of the target. The emulator’s geometry is adaptively updated
and subsequently used to inform local proposals. Unlike in adaptive
Markov chain Monte Carlo, continuous adaptation does not compromise
convergence of the sampler. KSMC combines the strengths of sequental
Monte Carlo and kernel methods: superior performance for multimodal
targets and the ability to estimate model evidence as compared to Markov
chain Monte Carlo, and the emulator’s ability to represent targets that
exhibit high degrees of nonlinearity. As KSMC does not require access to
target gradients, it is particularly applicable on targets whose gradients
are unknown or prohibitively expensive. We describe necessary tuning
details and demonstrate the benefits of the the proposed methodology on
a series of challenging synthetic and real-world examples
Intrinsic time gravity and the Lichnerowicz-York equation
We investigate the effect on the Hamiltonian structure of general relativity
of choosing an intrinsic time to fix the time slicing. 3-covariance with
momentum constraint is maintained, but the Hamiltonian constraint is replaced
by a dynamical equation for the trace of the momentum. This reveals a very
simple structure with a local reduced Hamiltonian. The theory is easily
generalised; in particular, the square of the Cotton-York tensor density can be
added as an extra part of the potential while at the same time maintaining the
classic 2 + 2 degrees of freedom. Initial data construction is simple in the
extended theory; we get a generalised Lichnerowicz-York equation with nice
existence and uniqueness properties. Adding standard matter fields is quite
straightforward.Comment: 4 page
Parameterized Inapproximability of Target Set Selection and Generalizations
In this paper, we consider the Target Set Selection problem: given a graph
and a threshold value for any vertex of the graph, find a minimum
size vertex-subset to "activate" s.t. all the vertices of the graph are
activated at the end of the propagation process. A vertex is activated
during the propagation process if at least of its neighbors are
activated. This problem models several practical issues like faults in
distributed networks or word-to-mouth recommendations in social networks. We
show that for any functions and this problem cannot be approximated
within a factor of in time, unless FPT = W[P],
even for restricted thresholds (namely constant and majority thresholds). We
also study the cardinality constraint maximization and minimization versions of
the problem for which we prove similar hardness results
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